As Venezuela prepares to elect a new president, the focus has turned to whether Chávez's legacy – a petroleum-fueled political-economic system he referred to as socialism for the 21st century – can last.

Caracas, Venezuela — Venezuela's seasonal downpours used to open a small river that flowed through Amada Quintana's dirt-floor house perched on a hillside slum here. But President Hugo Chávez fixed that. Workers from one of his poverty-fighting Bolivarian Missions came to her home, poured concrete floors, attached a sturdy roof, and rebuilt cracked walls.

Other programs he created provided her a free basic education and set her up with a government pension, even though she never paid into a retirement account. She receives $300 a month, more than enough to cover expenses.

For poor Venezuelans like Ms. Quintana, there were few things Mr. Chávez didn't fix.

Chávez, whose death was announced March 5, built his legend among the poor by providing free health care, education, and housing alongside subsidized gasoline, food, and even washing machines and stoves. He made friends abroad in largely the same way, sending countries oil shipments under preferential terms under the Petrocaribe agreement [See related story here].

However, cracks have appeared in that system. An economy that should otherwise be swimming in oil wealth is instead facing a potential shortage of cash. Venezuela, the country with the world's largest petroleum reserves, is producing less oil than it did when Chávez took office 14 years ago. Meanwhile, more and more of that oil money has gone to propping up the energy sectors in foreign countries or investing in domestic social programs.

As the country prepares to elect a new president on April 14, the focus has turned to whether Chávez's legacy – a petroleum-fueled political-economic system he referred to as socialism for the 21st century – can last.

"Whatever is resolved in the next election, the winner will face economic problems.... There's a structural problem here," says Caracas-based economist Leonardo Vera, a professor at Central University of Venezuela.

To close the fiscal gap, the incoming government might have to target the wildly popular programs at home or the petroleum aid it sends abroad. Neither move would be popular.

"The next administration will have to make adjustments," Mr. Vera says. "The question is what do you do?"

Figuring that out will likely fall to interim President Nicolás Maduro, Chávez's chosen successor. Mr. Maduro, an uncharismatic former bus driver who rose through the ranks of Venezuela's Socialist Party to become vice president under Chávez, is the front-runner in the April election.

Riding Chávez's political coattails to victory may be the easy part. Preserving the system that has kept happy the 55 percent of the country that reelected Chávez last fall will be the challenge. Maduro's tenuous support within the country makes it unlikely that he'd touch domestic spending, like the programs that helped Quintana rebuild her home and receive a basic education.

In an interview with a Venezuelan television station, Energy Minister Rafael Ramírez said, "We are not going to change one iota of the fundamental themes of Chávez's policies."

"The problem is that Venezuela is captured in a political trap," Vera says. "The country needs to make adjustments to make it sustainable, but there are no political incentives."

Foreign oil aid and domestic programs are "so fundamental to what Chávez stood for, both nationally and internationally," says George Ciccariello-Maher, a professor at Drexel University in Philadelphia and author of "We Created Chávez: A People's History of the Venezuelan Revolution."

"[Maduro] has to continue them."

Venezuela sits on a sea of oil; with the world's largest proven reserves of nearly 300 billion barrels it tops even Saudi Arabia.

Roughly 95 percent of Venezuela's foreign income – money derived from exports – comes from petroleum. Crude oil is trading at above $90 per barrel, more than 10 times the price of oil when Chávez took office. Chávez himself was instrumental in driving the price up, pushing oil-producing nations to stick to production quotas. And few reading tea leaves see the price dipping much in at least the next year.

But Chávez managed the resource differently than other leaders of oil-producing nations.

Instead of inviting foreign companies to tap the black gold, he largely kicked them out, increasing state control over the already nationalized industry. He then struck deals with foreign countries, sending them petroleum in exchange for goods and services.

In exchange for oil, China sent billions of dollars in loans. Cuba sends doctors to repay its petroleum debt. The Dominican Republic sends beans. Meanwhile, oil production has fallen, dropping by around 25 percent since 2001.

"We're giving away between 20 and 25 percent of our oil. We send it out and get no money in return," Vera says. "As a result, PDVSA [the state-owned oil and natural gas company] cannot generate enough revenue. So it fails to send the government enough [US] dollars, which adds to the currency problems."

Venezuela has tried to wean itself from surviving on oil revenue only, but with little success. Efforts to bolster the agricultural sector have been unsuccessful. The vast majority, founded in hopes of boosting production, ended up failing. The expropriation of large swaths of farmland from foreign companies, who were said to be underutilizing it, failed to help increase agricultural production, and even decreased it in some cases. And manufacturing, while growing, is still a tiny segment of the economy.

"The key question is whether the incoming administration can diversify the economy," says Mr. Ciccariello-Maher.

The next administration will likely look to deepen its relationship with China – to which it sends about 430,000 barrels per day – and Russia (although the United States is the largest buyer of Venezuelan crude). The terms of the deals Venezuela wants to strike with Russia and China are unclear, but the increase could help chip away at the currency shortage because the oil shipments are paid in US dollars.

While Chávez detractors say the country faces ruin, some also say the main criticisms lobbed against the government may be overcooked.

High rates of inflation have plagued Venezuela for decades, reaching 50 percent and 36 percent in the two years before Chávez took office, according to the United Nations Economic Commission for Latin America and the Caribbean. It averaged around 22 percent during Chávez's rule.

The shortages of food items seem to be more of a political sticking point than a problem for Venezuelans.

"We maybe have less variety than we used to, but it's not like it's causing people to go hungry," says Ana Frías, a mother of three here.

Yet the budget deficit – estimated at 7.4 percent of gross domestic product in 2012, according to the International Monetary Fund – and several currency devaluations are signs of structural problems.

Under Chávez, Venezuela devalued its currency seven times, most recently in February when it cut it to 6.3 bolívares per US dollar. Venezuela's currency continues to lose ground to the dollar, feeding a black market for the greenback that puts the value of US dollars at four times higher than the official exchange rate.

"We need to scrap the situation we have now wherein we are creating the illusion of prosperity by putting oil revenues in people's hands so they can think they're rich instead of actually investing in infrastructure," Mr. Bottome says.

However, to address shortages and compete with the black market for currency, Maduro's interim government this month said it would open a type of parallel market for US dollars. It plans to auction dollars to the private sector so it can import goods that have disappeared from store shelves. While minor, the decision is one sign that the Maduro government may make changes to the system Chávez left behind.

There is little hope that Maduro will be able to succeed where Chávez failed when it comes to the economy.

"He's not Chávez, and doesn't have his skills," Bottome says. "I think we'll see more of the status quo; Venezuela will limp along economically."

The foreign oil deals are seemingly the most obvious choice for a cut. But Maduro, if he wins in April, would be picking a fight with Cuba if he tries to reduce the amount of oil sent there. (Henrique Capriles, the opposition candidate, on the other hand, announced this month that if elected, "not another drop of oil will go toward financing the government of the Castros." The latest polling data places Maduro 14 percentage points ahead of Mr. Capriles.)

Observers say the Cuban advisers that Chávez long counted on are likely to heavily influence Maduro. The Castro brothers, whom Chávez considered friends and mentors, will play an oversized role in the Maduro administration, says Eric Hershberg, director of the Center for Latin American and Latino Studies at American University in Washington.

"Despite its problems, one thing you can say about the Cubans is that they are survivors," Mr. Hershberg says. "They've been able to take on everything, and they keep going."

Communist Cuba has survived for five decades, however, in part because it always had support from elsewhere. First it was Russia, then more recently Venezuela.

Will Venezuela need to find a benefactor, too?

"Maybe Venezuela can be its own savior," Hershberg says. "I think that's the big question."